Thompson threw scoring passes of 7 yards and 34 yards and Chancellor had rushing touchdowns from 3 and 15 yards as the Mean Green (9-4) put the game away with a 29-point second half.
Caleb Herring and Marcus Sullivan teamed for a 9-yard scoring pass play midway through the first period that gave UNLV (7-6) the first lead but North Texas scored the next 28 points to take command.
Antoinne Jimmerson forced his way in from 1-yard out late in the first quarter to tie the score for the Mean Green and a Thomson-to-Drew Miller 7-yard scoring play at the 6:07 mark of the third period gave North Texas the lead.
Chancellor increased the lead 4 seconds into the fourth period and, 8 minutes later, Thompson found Darnell Smith with a 34-yard play that was worth a 28-7 North Texas lead.
Herring completing a 13-yard pass to Jerry Rice Jr. with 4:56 to go but Chancellor put the game away with his 15-yard scoring run late in the final quarter.
The formal name of the game is the Heart of Dallas Bowl presented by PlainsCapital Bank.